Question

Point h is between g and i. If gh = 2x2 + 7x, hi = 9x – 2, and gi = 38, find the length of gh, hi and the possible values of x.

Answer 1

2x²+7x+9x-2=38
2x²+16x-40=0
2(x²+8x-20)=0
2(x+10)(x-2)=0
x=-10 or x=2
if we let x=-10 we get negative lengths for some of the segments which is not allowed so discard it. for x=2,

gh=22, hi=16, and gi=38